The ERC Grant "Analysis of moving incompressible fluid interfaces
", leaded by Francisco Gancedo
, offers a 2-year Ph.D. position.
The call will be open on 15th May 2018.
The deadline will be 22:00h on 10th June 2018.
The salary is competitive and teaching duties are up to the candidate.
This call could be declared void if no applicant meets the necessary conditions
The applicants should send an e-mail to "firstname.lastname@example.org
" with the subject: ERC pre doc application + "last name of the applicant" and the following documentation:
- A curriculum vitae
- Academic record
- Two recommendation letters (Professors must send these letters directly to email@example.com, with the subject: Recommendation letters+"last name of the applicant")
The research of this proposal is focused on solving problems that involve the evolution of fluid interfaces. The project will investigate the dynamics of free boundaries arising between incompressible fluids of different nature. The main concern is well-posed scenarios which include the possible formation of singularities in finite time or lack thereof, existence of solutions for all time. These contour dynamics issues are governed by fundamental fluid mechanics equations such as the Euler, Navier-Stokes, Darcy and quasi-geostrophic systems. They model important problems such as water waves, viscous waves, Muskat, interface Hele-Shaw and SQG sharp front evolution. All these contour dynamics frameworks will be studied with emphasis on singularity formation and global existence results, not only for their importance in mathematical physics, but also for their mathematical interest. These ones present huge challenges which will in particular require the use of different tools and methods from several areas of mathematics. The main goal of this project is to delve into and expand analytical techniques to go beyond the state of the art in these contour dynamics problems for incompressible fluids.